Electron. J. Diff. Eqns., Vol. 2006(2006), No. 64, pp. 1-9.

A boundary blow-up for sub-linear elliptic problems with a nonlinear gradient term

Zhijun Zhang

Abstract:
By a perturbation method and constructing comparison functions, we show the exact asymptotic behaviour of solutions to the semilinear elliptic problem
$$ \Delta u -|\nabla u|^q=b(x)g(u),\quad u>0 \quad\text{in }\Omega, \quad u\big|_{\partial \Omega}=+\infty, $$
where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with smooth boundary, $q\in (1, 2]$, $g \in C[0,\infty)\cap C^1(0, \infty)$, $g(0)=0$, $g$ is increasing on $[0, \infty)$, and $b$ is non-negative non-trivial in $\Omega$, which may be singular or vanishing on the boundary.

Submitted February 5, 2006. Published May 20, 2006.
Math Subject Classifications: 35J60, 35B25, 35B50, 35R05.
Key Words: Semilinear elliptic equations; large solutions; asymptotic behaviour.

Show me the PDF file (225K), TEX file, and other files for this article.

Zhijun Zhang
Department of Mathematics and Information Science
Yantai University, Yantai, Shandong, 264005, China
email: zhangzj@ytu.edu.cn

Return to the EJDE web page